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9-12 Geometry Unit 7 Lesson 7

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 •Unit 7 Unit 8

Modeling Prompts

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 •Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14

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Unit 7, Lesson 7

Circles in Triangles

Geometry

Practice

Problem 1
Student Task Statement
Triangle is shown with its incenter at . The inscribed circle’s radius measures 2 units. The length of is 9 units. The length of is 10 units. The length of is 17 units.

Triangle ABC with a circle inside with center D. Line segments AD and CD. Dashed line segment DF labeled 2. Dashed line segments DG and DE unlabeled. Line AB = 9. Line BC = 10. Line AC = 17.

What is the area of triangle ?

What is the area of triangle ?

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Problem 2

Student Task Statement

Triangle is shown with an inscribed circle of radius 4 units centered at point . The inscribed circle is tangent to side at the point . The length of is 6 units and the length of is 8 units. What is the measure of angle ?

<p>Triangle ABC with a circle inside with center D. Dashed lines from D to outside of circle, one labeled 4. AG = 6. BG = 8.</p>

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Problem 3

Student Task Statement

Construct the inscribed circle for the triangle.

<p>Triangle ABC</p>

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Problem 4

ForLesson 6: A Special Point

Student Task Statement

Point lies on the angle bisector of angle . Point lies on the perpendicular bisector of side .

What can we say about the distance between point and the sides and vertices of triangle ?
What can we say about the distance between point and the sides and vertices of triangle ?

<p>Triangle A B C. Dotted angle bisector drawn from C to A B, with point D. Second dotted angle bisector, drawn to right of other bisector, passing through A B and B C, with point E.</p>

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Problem 5

ForLesson 6: A Special Point

Student Task Statement

Construct the incenter of the triangle. Explain your reasoning.

<p>Triangle ABC</p>

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Problem 6

ForLesson 5: Triangles in Circles

Student Task Statement

The angles of triangle measure 30 degrees, 40 degrees, and 110 degrees. Will its circumcenter fall inside the triangle, on the triangle, or outside the triangle? Explain your reasoning.

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Problem 7

ForLesson 4: Quadrilaterals in Circles

Student Task Statement

The images show two possible blueprints for a park. The park planners want to build a water fountain that is equidistant from each of the corners of the park. Is this possible for either park? Explain or show your reasoning.

<p>Quadrilateral with interior angles =57, 128, 100, and 75 degrees </p> — park A

<p>Quadrilateral with interior angles = 75, 133, 105, and 47 degrees </p> — park B

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Problem 8

ForLesson 16: Weighted Averages in a Triangle

Student Task Statement

Triangle has vertices at and . What is the point of intersection of the triangle’s medians?

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Lesson 7 Resources

Student Materials